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Elena L [17]
4 years ago
13

Suppose that twelve bats was used in the experiment. For each trail, the zoo keeper pointed to one of two "feeders". Suppose tha

t the bats went to the correct feeder one that the zoo keeper pointed at) 9 times. Find the 95% confidence interval for the population proportion of times that the bat would follow the point.
a) 0.505,0.995
b) 0.32, 0.81
c) 046, 091
Mathematics
1 answer:
Marat540 [252]4 years ago
4 0

Answer:

a) 0.505,0.995

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 12, \pi = \frac{9}{12} = 0.75

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 - 1.96\sqrt{\frac{0.75*0.25}{12}} = 0.505

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.75 + 1.96\sqrt{\frac{0.75*0.25}{12}} = 0.995

So the correct answer is:

a) 0.505,0.995

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